What is the inverse of (ln(x))/(1-(ln(x))^2) ?

The inverse of (ln(x))/(1-(ln(x))^2) is e^{-(1+sqrt(1+4x^2))/(2x)},e^{-(1-sqrt(1+4x^2))/(2x)}

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inverse of (ln(x))/(1-(ln(x))^2)

inverse

\frac{ln ( x )}{1 - ( ln ( x ) ) ^{2}}

e^{- \frac{1 + 1 + 4 x ^{2}}{2 x}}, e^{- \frac{1 - 1 + 4 x ^{2}}{2 x}}

Solution steps

y = \frac{ln ( x )}{1 - ln ^{2} ( x )}

Replace

x

with

y

x = \frac{ln ( y )}{1 - ln ^{2} ( y )}

Solve for

y, x = \frac{ln ( y )}{1 - ln ^{2} ( y )}

e^{- \frac{1 + 1 + 4 x ^{2}}{2 x}}, e^{- \frac{1 - 1 + 4 x ^{2}}{2 x}}

y = \frac{2 ^{x}}{1 + 2 ^{x}}

f (x) = \frac{5 x - 3}{4 x + 7}

f (x) = e^{x + 9} - 2

\frac{6}{x - 1}

f (x) = \frac{7 x}{x - 1}

What is the inverse of (ln(x))/(1-(ln(x))^2) ?
The inverse of (ln(x))/(1-(ln(x))^2) is e^{-(1+sqrt(1+4x^2))/(2x)},e^{-(1-sqrt(1+4x^2))/(2x)}